Stabilizing Ship Motion With a Dual System Inertial Disk

Norwegian industries are constantly assessing new technologies and methods for more efficient and safer maintenance in the aqua cultural, renewable energy, and oil and gas industries. These Norwegian offshore industries share a common challenge: to install new equipment and transport personnel in a safe and controllable way between ships, farms and platforms. This paper deploys the Moving Frame Method (MFM) to analyze ship stability moderated by a dual gyroscopic inertial device. The MFM describes the dynamics of the system using modern mathematics. Lie group theory and Cartan’s moving frames are the foundation of this new approach to engineering dynamics. This, together with a restriction on the variation of the angular velocity used in Hamilton’s principle, enables an effective way of extracting the equations of motion. This project extends previous work. It accounts for the dual effect of two inertial disk devices, it accounts for the prescribed spin of the disks. It separates out the prescribed variables. This work displays the results in 3D on cell phones. It represents a prelude to testing in a wave tank.

Modeling a Knuckle-Boom Crane Control to Reduce Pendulum Motion Using the Moving Frame Method

A Knuckle Boom Crane is a pedestal-mounted, slew-bearing crane with a joint in the middle of the distal arm; i.e. boom. This distal boom articulates at the ‘knuckle (i.e.: joint)’ and that allows it to fold back like a finger. This is an ideal configuration for a crane on a ship where storage space is a premium. This project researches the motion and control of a ship mounted knuckle boom crane to minimize the pendulum motion of a hanging load. To do this, the project leverages the Moving Frame Method (MFM). The MFM draws upon Lie group theory — SO(3) and SE(3) — and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. The work reported here accounts for the masses and geometry of all components, interactive motor couples and prepares for buoyancy forces and added mass on the ship. The equations of motion are solved numerically using a 4th order Runge Kutta (RK4), while solving for the rotation matrix for the ship using the Cayley-Hamilton theorem and Rodriguez’s formula for each timestep. This work displays the motion on 3D web pages, viewable on mobile devices.

Modelling Buoy Motion at Sea

This project creates a model to assess the motion induced on a buoy at sea, under wave conditions. We use the Moving Frame Method (MFM) to conduct the analysis. The MFM draws upon concepts and mathematics from Lie group theory — SO(3) and SE(3) — and Cartan’s notion of Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. This work accounts for the masses and geometry of all components and for buoyancy forces and added mass. The resulting movement will be displayed on 3D web pages using WebGL. Finally, the theoretical results will be compared with experimental data obtained from a previous project done in the wave tank at HVL.

Production and Analytics of a Multi-Linked Robotic System

This paper extends research into flexible robotics through a collaborative, interdisciplinary senior design project. This paper deploys the Moving Frame Method (MFM) to analyze the motion of a relatively high multi-link system, driven by internal servo engines. The MFM describes the dynamics of the system and enables the construction of a general algorithm for the equations of motion. Lie group theory and Cartan’s moving frames are the foundation of this new approach to engineering dynamics. This, together with a restriction on the variation of the angular velocity used in Hamilton’s principle, enables an effective way of extracting the equations of motion. The result is a dynamic 3D analytical model for the motion of a snake-like robotic system, that can take the physical sizes of the system and return the dynamic behavior. Furthermore, this project builds a snake-like robot driven by internal servo engines. The multi-linked robot will have a servo in each joint, enabling a three-dimensional movement. Finally, a test is performed to compare if the theory and the measurable real-time results match.

Modelling the Motion of a 2-Arm ROV

Norway conducts operations on a variety of structures in the North Sea; e.g. oilrigs, monopole windmills, subsea trees. These structures often require subsea installation, observation, and maintenance. A remotely operated vehicle (ROV) can assist in these operations. Automation of intended motion is the desired goal. This paper researches the motion of an ROV induced by the motion of the robotic manipulators, motor torques, and added mass of fluid. This project builds upon a previous project that had one robotic arm; this time, there are two, but the method is unchanged. Furthermore, this work explores both the patterns in addressing such challenges, and an improved integration scheme. This research uses the Moving Frame Method (MFM) to carry out this project. In fact, this paper demonstrates the ease with which the MFM is extensible. Notable is that this work represents an international collaboration between an engineering school in Norway and one in the US. This work invites further research into improved numerical methods, solid/fluid interaction and the design of Autonomous Underwater Vehicles (AUV). AUVs beckon an era of Artificial Intelligence when machines think, communicate and learn. Rapidly deployable software implementations will be essential to this task.

The Complete Set of Independent Affine Moment Invariants of Color Images

Moment invariants of images are important features for pattern recognition and image processing. Many methods have been proposed to derive moment invariants of images under different group actions. However, the completeness and independence of a set of moment invariants are two open problems. In this paper, we use the moving frame method to derive affine moment invariants of color images. The moving frame for the normalized color moment space under the action of the affine group is presented. Using this moving frame, we obtain a complete and independent set of affine moment invariants of color images. This system of affine moment invariants is also invariant under diagonal photometric changes. Experimental results are provided to validate the correctness of the derivation.

Modeling Crane-Induced Ship Motion Using the Moving Frame Method

A decline in oil-related revenues challenges Norway to focus on new types of offshore installations. Often, ship-mounted crane systems transfer cargo or crew onto offshore installations such as floating windmills. This project analyzes the motion of a ship induced by an onboard crane in operation using a new theoretical approach to dynamics: the moving frame method (MFM). The MFM draws upon Lie group theory and Cartan's moving frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. While others have applied aspects of these mathematical tools, the notation presented here brings these methods together; it is accessible, programmable, and simple. In the MFM, the notation for multibody dynamics and single body dynamics is the same; for two-dimensional (2D) and three-dimensional (3D), the same. Most importantly, this paper presents a restricted variation of the angular velocity to use in Hamilton's principle. This work accounts for the masses and geometry of all components, interactive motor couples and prepares for buoyancy forces and added mass. This research solves the equations numerically using a relatively simple numerical integration scheme. Then, the Cayley–Hamilton theorem and Rodriguez's formula reconstruct the rotation matrix for the ship. Furthermore, this work displays the rotating ship in 3D, viewable on mobile devices. This paper presents the results qualitatively as a 3D simulation. This research demonstrates that the MFM is suitable for the analysis of “smart ships,” as the next step in this work.